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A connectionist model of a continuous developmental transition in the balance scale task

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A connectionist model of a continuous developmental transition in the balance scale task
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   Connectionist Model 1 Running head: CONNECTIONIST MODEL OF THE BALANCE SCALE TASK A Connectionist Model of a Continuous Developmental Transition in the Balance Scale Task Anna C. Schapiro and James L. McClelland Stanford University   Connectionist Model 2 Abstract A connectionist model of the balance scale task is presented which exhibits developmental transitions between ‘Rule I’ and ‘Rule II’ behavior (Siegler, 1976) as well as the ‘catastrophe flags’ seen in data from Jansen & van der Maas (2001). The model extends the McClelland (1989, 1995) model of this task by introducing intrinsic variability into processing and by allowing the network to adapt during testing in response to its own outputs. The simulations direct attention to several aspects of the experimental data indicating that children generally show gradual change in sensitivity to the distance dimension on the balance scale. While a few children show larger changes than are characteristic of the model, its ability to account for nearly all of the data using continuous processes is consistent with the view that the transition from Rule I to Rule II  behavior is typically continuous rather than discrete in nature. Key Words: Development, stage transitions, connectionist models, balance scale task   Connectionist Model 3 A Connectionist Model of a Continuous Developmental Transition in the Balance Scale Task What is the nature of the underlying knowledge representation that determines  patterns of performance and developmental change in children? This question has inspired an enormous amount of empirical and theoretical work aimed at inferring mechanisms of development based on children’s behavior. One window into these developmental mechanisms that has been used extensively is children’s performance on the balance scale task. Interpretations of the data from this task have tapped into a greater debate in cognitive science between two perspectives. At one end of the spectrum is what we will call the rule-based approach, which holds that performance in tasks like the  balance scale task is based on a small number of distinct and discrete rules that can be used to generate responses to test items. Development consists of a progression through the use of a sequence of these rules. In this view, children’s behavior is not simply describable by rules but is actually caused by the use of explicit rule representations, e.g., through the retrieval of an explicit rule from long-term memory to be used in a task (Kerkman & Wright, 1988). At the other end of the spectrum is what we will call the continuous perspective, which holds that information is represented in a more graded manner that is only approximately characterizable by the kinds of rules in rule-based approaches, and transitions between stable stages of performance are not in fact so abrupt when considered carefully. Connectionist models provide a possible mechanism for this continuous change, in which knowledge is stored as the weights of connections between   Connectionist Model 4 simple neuron-like processing units. Rule-like behavior in a task like the balance scale task emerges from small incremental changes in the weights between these processing units, which in turn lead to incremental changes in units’ activations. In the connectionist and, more generally, the continuous approach, apparent qualitative change need not reflect a discrete transition; behavior that might sometimes look like rule change is seen as arising from incremental change in what is underlyingly continuous processing. Though connectionist models can approximate to an arbitrary degree of accuracy the rule-like behavior of a system that explicitly incorporates rules into knowledge representation, the rule-based and continuous approaches have different tendencies in their behavior that do not motivate identical empirical predictions. For example, especially in periods of transition, a continuous model predicts that there will tend to be graded sensitivity to the dimensions relevant to the transition, whereas a strict rule-based approach predicts that sensitivity to a particular dimension will either be present or absent. The question we address here is whether there is indeed the kind of graded sensitivity that would be expected from the kinds of transitions that tend to occur in continuous models. We consider an elaborated version of McClelland’s (1989, 1995) connectionist model of the balance scale task and compare it in detail to aspects of the relevant experimental data. The model is used to account for the patterns of performance found in an extensive investigation of transitions in balance scale task performance by Jansen and van der Maas (2001), bringing out aspects of the empirical data that indicate continuity in transition.   Connectionist Model 5  Balance scale task In the balance scale task, developed srcinally by Inhelder and Piaget (1958; Piaget & Inhelder, 1969), children are shown a balance scale with a varying number of weights placed on pegs on each side, at varying distances from the fulcrum (see Figure 1). While the movement of the scale is prevented, the children are asked to imagine what would happen if the scale were allowed to move freely; they indicate whether they think the left or right side of the scale would fall, or whether the two sides would be in balance.  Figure 1 . The type of scale used in the balance scale task. Siegler (1976, 1981) adopted the balance-scale paradigm to test whether children’s behavior on the task is best described by the use of rules. He used six item types: balance, weight, distance, conflict-weight, conflict-distance, and conflict-balance. Children were classified as using a particular rule based on their responses to test items of each of these different types. Balance items have the same number of weights at the same distance from the fulcrum on each side. Weight items have different numbers of weights on each side at the same distance from the fulcrum. Distance items have the same number of weights at different distances. Conflict items have fewer weights at a greater distance on one side of the fulcrum and more weights at a smaller distance on the other. In conflict-weight items, the correct answer is that the side with more weight falls. In
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